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FCI Assisstatn Grade III questions with answers for practice
FCI Arithmetical Ability
1. The product of 2 numbers is 1575 and their quotient is 9/7. Then the sum of the numbers is –
a. 74
b. 78
c. 80
d. 90
Ans : Let the numbers be x and y .
∴ xy = 1575
And x/y = 9/7
∴ xy/x/y = 1575/9/7
∴ y2 = 1225
∴ y = 35 and x = 45
∴ The sum of the numbers = 45+35
= 80
2. The value of (81)3.6 * (9)2.7/ (81)4.2 * (3) is __
a. 3
b. 6
c. 9
d. 8.2
Ans : (81)3.6 * (9)2.7/(81)4.2 * (3) = (3)14.4 * (3)5.4/(3)16.8 * (3)
= 314.4+5.4-16.8-1
= 32
= 9
3. √6+√6+√6+… is equal to –
a. 2
b. 5
c. 4
d. 3
Ans : Let √6+√6+√6+…. be x.
∴ x =√6+x
∴ x2 = 6+x
∴ x2 + x – 6 = 0
∴ (x-3) (x+2) = 0
∴ x = 3
4. The sum of the squares of two natural consecutive odd numbers is 394. The sum of the numbers is –
a. 24
b. 32
c. 40
d. 28
Ans : Let the consecutive odd numbers be x and (x+2)
? x2 + (x + 2)2 = 394
∴ x2 + x2 + 4x + 4 = 394
∴ 2 x2 +4x – 390 = 0
∴ x2 + 2x – 195 = 0
∴ (x +15) (x-13) = 0
∴ x = 13
∴ Required sum = 13 +15 =28
5. When (6767 +67) is divided by 68, the remainder is-
a. 1
b. 63
c. 66
d. 67
Ans: (6767+ 67) = 67(6766 + 166)
As 66 is an even number
∴ 6766 is an even number
∴ (6766 + 1) is perfectly divisible by (67 + 1)
i.e. 68
∴ The remainder = 67
6. In a division sum, the divisor is 4 times the quotient and twice the remainder. If a and b are respectively the divisor and the dividend then-
a. 4b-a2 /a =3
b. 4b-2a /a2 =2
c. (a+1)2 = 4b
d. A(a+2)/b = 4
Ans : As divisor is a, and dividend is b.
∴ Quotient = a/4
And Remainder = a/2
∴ b = a * a/4 + a/2
∴ 4b = a2 + 2a
∴ a(a+2)/b = 4
7. If 738 A6A is divisible by 11, then the value of A is-
a. 6
b. 3
c. 9
d. 1
Ans : As 738A6 A is divisible by 11.
∴ A + A + 3 = 6 + 8 + 7
∴ A = 9
8. The east positive integer that should be subtracted from 3011 * 3012 so that the difference is perfect square is-
a. 3009
b. 3010
c. 3011
d. 3012
Ans : ? 3011 * 3012 = 3011 (3011 + 1)
= (3011)2 + 3011
∴ Required least number = 3011
9. P, Q, R are employed to do a work for Rs. 5750. P and Q together finished 19/23 of work and Q and R together finished 8/23 of work. Wage of Q, in rupees, is-
a. 2850
b. 3750
c. 2750
d. 1000
Ans : Work done by Q = 19/23 + 8/23 – 1
4/23
∴ Wage of Q = 4/23 * 5750
= Rs. 1000
10. A can do a piece of work in 24 day, B in 32 days and C in 64 days. All begin to do it together, but A leaves after 6 days and B leaves 6 days before the completion of the work. How many days did the work last?
a. 15
b. 20
c. 18
d. 30
Ans : Work done by A = 6/24 = ¼
Work done by B = (x-6)/32
(where x is no. of days in which work is competed)
? ¼ + x – 6/32 + x/64 = 1
∴ 16 + 24 – 12 + x /64 = 1
∴ 3x + 4 = 64
∴ x = 60/3 = 20 days
11. The square root of (0.75)3 /1-0.75 + [0.75 + 90.75)2 +1] is-
a. 1
b. 2
c. 3
d. 4
Ans : The square root of
[(0.75)3/1 – 0.75 + {0.75 + (0.75)2 + 1}]
= √1.6875 + 2.3125
=√4
= 2
12. Given that √4096 = 64, the value of √4096 + √40.96 +√0.004096 is-
a. 70.4
b. 70.464
c. 71.104
d. 71.4
Ans : Given Exp. = √4096 + √40.96 +√0.004096
= 64 + 6.4 + 0.064
= 70.464
13. By selling an article at 3/4th of the marked price, there is a gain of 25%. The ratio of the marked price and the cost price is-
a. 5 : 3
b. 3 : 5
c. 3 : 4
d. 4 : 3
Ans : Let of M.P. be Rs. x.
∴ S.P. = Rs.3x/4
and C.P. = 3x/4 * 100/125
= Rs.3x/5
∴ required ratio = x: 3x/5
= 5:3
14. A and B earn in the ratio 2:1. They spend in the ratio 5:3 and save in the ratio 4:1. If the total monthly savings of both A and B are Rs.5,000, the monthly income of B is-
a. Rs.7,000
b. Rs.14,000
c. Rs.5,000
d. Rs.10,000
Ans : Let the monthly income of B be Rs. x.
∴ Monthly income of A = Rs. 2x and
Saving of A =5000 * 4/(4 + 1)
= Rs. 4000
Saving of B = Rs.1000
? 2x – 4000/x-1000 = 5/3
⇒ 6x – 12000 = 5x – 5000
∴ x = Rs.7000
15. The ratio of the sum of two numbers and their difference is 5:1. The ratio of the greater number to the smaller number is-
a. 2 : 3
b. 3 : 2
c. 5 : 1
d. 1 : 5
Ans : Let the numbers be x and y.
? x + y/ x – y = 5/1
⇒ 5x – 5y = x + y
⇒ 4x = 6y
⇒ x/y = 6/4
x : y = 3 : 2
16. A cistern has 3 pipes A, B and C. A and B can fill it in 3 and 4 hours respectively, and C can empty it in 1 hour. If the pipes are opened at 3 p.m., 4 p.m. and 5 p.m. respectively on the same day, the cistern will be empty at-
a. 7.12 p.m.
b. 7.15 p.m.
c. 7.10 p.m.
d. 7.18 p.m.
Ans : Let the cistern be emptied at x p.m.
? x -3/3 + x – 4/4 = x - 5/1
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